7x^2+62x+15=0

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Solution for 7x^2+62x+15=0 equation:


Simplifying
7x2 + 62x + 15 = 0

Reorder the terms:
15 + 62x + 7x2 = 0

Solving
15 + 62x + 7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
2.142857143 + 8.857142857x + x2 = 0

Move the constant term to the right:

Add '-2.142857143' to each side of the equation.
2.142857143 + 8.857142857x + -2.142857143 + x2 = 0 + -2.142857143

Reorder the terms:
2.142857143 + -2.142857143 + 8.857142857x + x2 = 0 + -2.142857143

Combine like terms: 2.142857143 + -2.142857143 = 0.000000000
0.000000000 + 8.857142857x + x2 = 0 + -2.142857143
8.857142857x + x2 = 0 + -2.142857143

Combine like terms: 0 + -2.142857143 = -2.142857143
8.857142857x + x2 = -2.142857143

The x term is 8.857142857x.  Take half its coefficient (4.428571429).
Square it (19.61224490) and add it to both sides.

Add '19.61224490' to each side of the equation.
8.857142857x + 19.61224490 + x2 = -2.142857143 + 19.61224490

Reorder the terms:
19.61224490 + 8.857142857x + x2 = -2.142857143 + 19.61224490

Combine like terms: -2.142857143 + 19.61224490 = 17.469387757
19.61224490 + 8.857142857x + x2 = 17.469387757

Factor a perfect square on the left side:
(x + 4.428571429)(x + 4.428571429) = 17.469387757

Calculate the square root of the right side: 4.179639668

Break this problem into two subproblems by setting 
(x + 4.428571429) equal to 4.179639668 and -4.179639668.


Subproblem 1
x + 4.428571429 = 4.179639668

Simplifying
x + 4.428571429 = 4.179639668

Reorder the terms:
4.428571429 + x = 4.179639668

Solving
4.428571429 + x = 4.179639668

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.428571429' to each side of the equation.
4.428571429 + -4.428571429 + x = 4.179639668 + -4.428571429

Combine like terms: 4.428571429 + -4.428571429 = 0.000000000
0.000000000 + x = 4.179639668 + -4.428571429
x = 4.179639668 + -4.428571429

Combine like terms: 4.179639668 + -4.428571429 = -0.248931761
x = -0.248931761

Simplifying
x = -0.248931761


Subproblem 2
x + 4.428571429 = -4.179639668

Simplifying
x + 4.428571429 = -4.179639668

Reorder the terms:
4.428571429 + x = -4.179639668

Solving
4.428571429 + x = -4.179639668

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.428571429' to each side of the equation.
4.428571429 + -4.428571429 + x = -4.179639668 + -4.428571429

Combine like terms: 4.428571429 + -4.428571429 = 0.000000000
0.000000000 + x = -4.179639668 + -4.428571429
x = -4.179639668 + -4.428571429

Combine like terms: -4.179639668 + -4.428571429 = -8.608211097
x = -8.608211097

Simplifying
x = -8.608211097


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.248931761, -8.608211097}

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